Plankton patchiness and its effect on larger-scale productivity

We investigate systematically the effect of small-scale biological and physical processes on the generation of plankton patchiness, and on the biological production averaged over scales much larger than those of the patches. We use an excitable reaction-diffusion model with one physical dimension and two biological compartments: zooplanktonic predators Z and phytoplanktonic prey P. It is assumed that the assimilation efficiency is of order 0.1. With sinusoidal initial conditions, the maximum in domain-averaged P is about six times that which would be estimated assuming spatial homogeneity. With random initial conditions similar enhancement factors are obtained and patches emerge of characteristic size, proportional to the square root of the diffusivity as in classical work on simpler systems. Both the patch size and the production show large variances across ensembles of integrations initialized randomly but with the same mean. For both sinusoidal and random initial conditions, the most extreme effect is obtained when the phytoplankton growth rate is between one and four times the rate of diffusion, and when the mean initial condition lies close to the excitation threshold; the effect of varying the initial conditions is also considered. A bi-stable version of the plankton dynamics produces a quasi-stable patchy state of the model with mean properties far from those of either equilibrium. These results illustrate both the desirability of high-resolution observations of plankton, and that caution is required in using 'mean field' plankton dynamics in large-scale biophysical models of the ocean.